Wages and employment:The role of occupational skills∗

Esther Mirjam Girsberger† Matthias Krapf‡

Miriam Rinawi§

January 29, 2019

Abstract

We study how skills acquired in vocational education and training (VET) affectwages and employment dynamics in Switzerland. We present and estimate a searchand matching model for workers with a VET degree who differ in their interpersonal,cognitive and manual skills. Assuming a match productivity which exhibits worker-job complementarity, we estimate how workers’ skills map into job offers, wagesand unemployment. Firms value cognitive skills on average almost twice as much asinterpersonal and manual skills. Moreover, they prize complementarity in cognitiveand interpersonal skills. We estimate average returns to VET skills in hourly wagesof 9%. Furthermore, VET improves labour market opportunities through higher jobarrival rate and lower job destruction. Workers thus have large benefits from gettinga VET degree.

Keywords: Occupational training, labour market search, multidimensional skills.JEL classification numbers: E23, J23, J24, J64.∗This study is partly funded by the Swiss Secretariat for Education, Research and Innovation through its

Leading House on the Economics of Education, Firm Behaviour and Training Policies. The study alsobenefitted from the support of the Swiss National Centre of Competence in Research LIVES - Over-coming vulnerability: Life course perspectives, which is financed by the Swiss National Science Foun-dation (grant number: 51NF40-160590), and from a SNSF Doc.Mobility Scholarship (project number:P1ZHP1_155498). We wish to thank Uschi Backes-Gellner, Chris Flinn, Miriam Gensowski, KalaivaniKarunanethy, Rafael Lalive, and Mark Lambiris for valuable comments on this as well as earlier versionsof this study. The views expressed in this study are the authors’ and do not necessarily reflect those of theSwiss National Bank.†University of Technology Sydney & IZA. Corresponding author. Contact: EstherMirjam.Girsberger@uts.edu.au. Address: UTS

Business School, Department of Economics, 14-28 Ultimo Rd, Ultimo NSW 2008, Australia. Phone: +61 2 9514 3371.‡University of Basel, Switzerland. Email: matthias.krapf@unibas.ch.§Swiss National Bank, Switzerland. Email: miriam.rinawi@snb.ch.

1 Introduction

When evaluating the effectiveness of education programmes in promoting labour mar-ket opportunities, a crucial question is whether the programmes should be vocationallyor generally oriented. Vocational programmes are often associated with a more smoothschool-to-work transition and with reduced levels of youth unemployment (Ryan, 2001;Scarpetta et al., 2010). Some scholars, however, caution that vocational education provesdisadvantageous later in life (Hanushek et al., 2017) or for technology-adoption in theeconomy (Krueger and Kumar, 2004a,b; Rendall and Weiss, 2016). What this debatelargely ignores is that vocational education allows workers to train in many different oc-cupations and hereby acquire different skill bundles. These different skill bundles areassociated with different labour market outcomes (Ingram and Neumann, 2006; Lindqvistand Vestman, 2011).

In this paper, we investigate how the skills acquired in vocational education and train-ing (VET) affect wages and employment dynamics. Furthermore, we examine whichskills are in high demand by firms. Finally, we attempt to quantify the value of the skillsacquired in VET for workers and firms. To do so, we present a simple search and match-ing model with workers and firms who differ in their multidimensional skill supply anddemand. A worker’s skill supply corresponds to the skills acquired during VET and re-mains constant over time. Firms use these skills in different combinations to produceoutput. We assume a simple linear production function in skills, with worker-job comple-mentarity and correlated skill demands. Workers and firms match randomly, they engagein Nash bargaining over wages and jobs are destroyed exogenously.

We take our model to the data combing labour force survey data with information onskills acquired during VET for Switzerland. VET is a very common education programmein a number of European countries. In Switzerland, around two thirds of a cohort enrolin VET and the system is considered to be among the best worldwide.1 Our skill datacomes from the Berufsinformationszentrum (BIZ), the state-led career-counselling cen-tre. BIZ provides a detailed list of skills that are used in individual vocational occupationson the 5-digit level, covering a total of 220 occupations. We group the single skills inthree broad categories, differentiating between interpersonal, cognitive and manual skills.For labour market outcomes we use the Social Protection and Labour Market (SESAM)survey. The SESAM consists of the Swiss Labour Force Survey, a representative panelsurvey, and register data on employment histories, unemployment benefits, and wages. To

1Switzerland regularly ranks among the top three nations at the World Skills Cham-pionship (see https://api.worldskills.org/resources/download/8742/9562/10479?l=en andhttps://www.worldskills.org/about/members/switzerland/).

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obtain VET workers’ skill bundles, we match the BIZ skills to the SESAM survey usingthe 5-digit occupational code of the learned occupation.

Our estimation results offer the following insights. Firms value all three skill dimen-sions, though to a different extent. The average productivity of cognitive skills is almosttwice as high (at 2.25 Swiss francs per hour) as the one of interpersonal (1.30 Swissfrancs) and manual skills (1.35 Swiss francs). Moreover, firms have a strong demand forcomplementarity in cognitive and interpersonal skills, and they tend to prefer either man-ual or non-manual specialists. The pattern of workers’ skill supply matches the firms’demand for skills fairly well.

To isolate and quantify the returns to skills, we compare the returns to VET with skillsto VET without skills in our simulation. We find the returns to skills to amount to 9%in hourly wages. However, VET not only offers returns to skills in terms of wages, italso improves labour market opportunities through higher job arrival rates and lower jobdestruction. Taking into account selection into VET, we find that workers without VETand only compulsory education would have returns to a VET degree of 11% in hourlywages. Most importantly, however, they would see their unemployment drop (as a resultof longer employment and shorter unemployment spells) and see their overall welfare in-crease by one third. Finally, a simple cost-benefit analysis reveals large benefits of VETfor workers, while benefits for firms could range from negative to positive, depending onthe underlying assumptions of the counterfactual scenario.

This paper ties into two strands of the literature. First, it contributes to the literatureon vocational education and labour market outcomes. Vocational education is associ-ated with facilitating school-to-work transitions and low youth unemployment (Plug andGroot, 1998; Ryan, 2001; Zimmermann et al., 2013; Eichhorst et al., 2015). However,evidence on longer-term labour market outcomes of vocational education is more scarceand more mixed (Dearden et al., 2002; Balestra and Backes-Gellner, 2017; Hanushek etal., 2017). Our paper also relates to the growing literature on the specificity of humancapital and returns to skills. Recent contributions suggest that the number of years of ed-ucation alone is not a sufficient measure of skill and propose an alternative measure basedon observed characteristics of jobs held by workers (Autor et al., 2003; Ingram and Neu-mann, 2006; Poletaev and Robinson, 2008; Lazear, 2009; Kambourov and Manovskii,2009; Gathmann and Schönberg, 2010; Eggenberger et al., 2018). A general finding isthat individuals move to occupations with similar skill requirements and that skills areclosely related to wages. While informative, a major shortcoming of this literature is thatit considers job transitions and wages separately.

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Our paper differs from these papers in two important aspects. First, our empiricalanalysis of labour market outcomes of VET workers makes use of a simple search andmatching model, in which labour market outcomes (i.e. employment and wages) are anequilibrium outcome of the demand and supply of VET labour. We rely on the frameworkdeveloped by Lise and Postel-Vinay (2016), but modify it in several aspects and apply itto a different context, the Swiss labour market for VET workers.2 Focusing not only onVET labour supply, but also modelling the demand for VET labour allows us to studysimultaneously the effect of skills on wages and employment. Moreover, it enables usto estimate both workers’ and firms’ benefit from VET. This is important for evaluatingthe overall value of a vocational education system. Second, we contribute to the studyof long-term labour market outcomes of VET workers. We distinguish in our analysisdifferent VET occupations according to their level of interpersonal, cognitive and manualskills. This refined analysis provides new insights into how different skills affect labourmarket outcomes differently. It turns out that not all VET occupations confer the samereturns in terms of wages and (to a lesser extent) employment perspectives.

The paper proceeds as follows. Section 2 provides information on VET in Switzer-land, discusses the data sources and presents descriptive evidence on interpersonal, cogni-tive and manual skills and labour market outcomes of VET workers. Section 3 presents asimple model of search and matching in the labour market with a multi-dimensional skillvector. This model allows us to jointly study wages and employment outcomes of VETworkers. Section 4 outlines our structural estimation procedure and discusses identifica-tion. Section 5 presents the estimation results, which form the basis of the simulations inSection 6 to estimate the value of VET. Section 7 concludes.

2 Institutional background and data

2.1 Institutional background

In Switzerland, compulsory school comprises nine years; six years of primary school andthree years of lower secondary school. Different school-type models exist at the lowersecondary level across and within cantons, though most models offer two or three tracks

2The main differences of our model are that workers’ skills do not adjust over time, there is no on-the-job search, and we rely on a production function with worker-job complementarity as in Lazear (2009).Despite a different focus and modelling choices, we find similar qualitative results in terms of the relativeproductivity of the different skills and the complementarity-specialisation patterns in the demand for skillsby firms as Lise and Postel-Vinay (2016) for the US.

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which differ in how intellectually demanding they are (i.e. upper-level, intermediate-levelor basic courses). Upon finishing lower secondary school, pupils can follow differentpathways.

For a general education, students attend the Gymnasium, for which they need to takean entry exam.3 At the end of the Gymnasium, they have completed general upper sec-ondary education (corresponding to 12 or 13 years of education) and are awarded with theuniversity entrance diploma.

For a vocational education and training (VET), students have to apply for an appren-ticeship position with a host firm. The apprenticeship is a dual programme that combinesformal education at a vocational school with on-the-job training at the host firm.4 Train-ing starts after completion of compulsory education and, depending on the occupation,lasts for three to four years. Skills acquired in vocational education are not firm-specific,but transferable across firms and occupations. The content taught in vocational schoolsand firms is formally regulated. Training quality is ensured by interim and final exami-nations based on common quality standards. The training content is regularly revised ina tripartite process, in which employer organisations, employee representatives, and thegovernment participate (Eggenberger et al., 2018).

Upon completion of the VET programme, successful students receive a nationallyrecognised diploma. They are not bound to their host firm, but can now freely movearound in the labour market. Indeed, the retention rate after graduation is only 35 per-cent (Schweri et al., 2003). Given that the Swiss educational system is characterised by ahigh degree of permeability, many workers with a VET diploma continue their educationalpathway by earning a university degree or taking further classes at a professional college.5

About 65 percent of a Swiss youth cohort enroll in VET. This share is larger than inany other country in which VET is available (Hanushek et al., 2017). In Switzerland, VETalso attracts high ability students because of its excellent reputation and promising careeropportunities.

3In many cantons, only pupils who attended an upper-level school track have access to the Gymnasium.Those with an intermediate-level track may repeat a completed school year in an upper-level track to getinto the Gymnasium.

4There exist also vocational schools (i.e. in business) which offer full-time vocational education in combina-tion with an internship of several months. This type of vocational education is relatively rare in Switzerland.

5Admission to a university or a university of applied sciences usually requires a special vocational diploma’Berufsmatura’, which can be obtained in parallel to the nationally recognised VET degree. Based on thelabour market data (SESAM), we estimate that around 20% of all VET graduates successfully complete aprofessional college/university of applied sciences (18.7%) or university (2.5%) later on.

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2.2 Data sources

Our analysis builds on two main data sources: First, we use data on skills taught inVET from the career-counselling centre Berufsinformationszentrum (BIZ) to constructoccupation-specific skill bundles. We describe this skill data source further below. Sec-ond, we use the Social Protection and Labour Market (SESAM) survey for labour marketoutcomes.

SESAM is a matched panel data set linking the Swiss Labour Force Survey (SLFS)with data from different social insurance registers. The SLFS is a nationally represen-tative, rotating household panel that offers a rich set of information on employment, so-ciodemographic, educational, and occupational characteristics. The matched social in-surance information provides the duration of individual employment and unemploymentspells, as well as monthly and yearly earnings and unemployment benefits.

Our observation period covers the years 2004 through 2009, for which SESAM of-fers consistent data. Each individual remains in the SESAM panel for five years or less.During our sample period the survey was run on a yearly basis in the second quarter. Itcontains questions both about the current situation as well as about the past. We restrictour analysis to a sample of male individuals who are between 20 and 64 years old andwho have obtained a VET degree as their highest education level.6 We exclude individu-als who are out of the labour force, but include part-time workers (who make up around10% of the sample). For the analysis, we compute hourly wages and trim the wage distri-bution below the bottom 4% and above the top 0.5%. We only keep those individuals inthe analysis for whom we observe at least two years of data. In total, our sample consistsof 5,050 individuals and 13,734 person-year observations.

2.3 Descriptive statistics and reduced-form evidence

2.3.1 Occupational skills

We use data from the career-counselling centre Berufsinformationszentrum (BIZ) to con-struct a measure of skills that are acquired during VET. BIZ provides a detailed list of

6By focusing on workers who have acquired different skill bundles within the same education level, we limitthe bias from selection into different education levels (Backes-Gellner and Wolter, 2010; Geel and Backes-Gellner, 2011). Appendix A provides some descriptive evidence from the Swiss TREE data on selection intovocational and general education tracks by cognitive abilities and personality traits of students. It shows thatstudents in vocational education are heterogeneous (as in other education pathways). Moreover, students inthe vocational track who subsequently enroll in tertiary education are similar in their characteristics to thosewith in the general education track, while those with only compulsory education resemble students in thevocational track who do not enroll in further studies at a later stage.

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skills which are acquired and used in each VET occupation. Apprentices studying for aVET occupation receive training in these skills and have to pass a standardised exam atthe end of their training period. The BIZ data covers a total of 220 VET occupations thatexisted during the period we examine. The list comprises 26 different skills, of which weuse 24.7 Each of these 24 skills is either classified as interpersonal (10 skills), cognitive (9skills), or manual (5 skills). Examples include ’ability to work in a team’ (interpersonal),’visual thinking’ (cognitive), and ’fine motor skills’ (manual).

These 24 skills represent 24 dimensions of skill heterogeneity across workers, result-ing in 224 = 16, 777, 216 different potential skill bundles. In order to reduce the dimen-sionality of the problem, we add up the number of acquired skills within each of the threeskill dimensions: interpersonal, cognitive and manual.8 Depending on the occupationin which VET students train, their acquired skill bundle differs substantially. For exam-ple, care professionals acquire only interpersonal skills (5 skills), IT-technicians acquiremostly cognitive skills (5 out of 7 skills), and car mechanics acquire mostly manual skills(3 out of 5 skills). There are many more VET occupations, some providing similar andothers providing more balanced skills bundles than these three examples.

Table 1 presents descriptive statistics on the skills of the 5,050 male workers with aVET degree in our sample.

Table 1: DESCRIPTIVE STATISTICS FOR WORKERS’ OCCUPATIONAL SKILLS.obs mean S.D. distribution of number of skills

Skill dimension 0 1 2 3 4 5

interpersonal 5,050 1.805 1.711 1,239 1,854 267 779 163 748cognitive 5,050 2.140 1.274 281 1,471 1,613 1,053 208 424manual 5,050 1.228 0.820 1,075 1,925 1,872 178

correlationinterp cogn manual

interpersonal 1.000cognitive 0.328 1.000manual -0.462 -0.261 1.000

The workers in our sample have acquired on average 1.81 interpersonal skills, 2.14cognitive skills and 1.23 manual skills. Each skill dimension has a different distribution.

7Based on the BIZ’s own classification, we exclude ’robust health’ and ’strong physique’ because they de-scribe physical attributes rather than skills that can be acquired.

8This implies that each skill within a skill dimension is equally valuable. Appendix B shows how our skillmeasure compares with O*Net-based measures used in the related literature.

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The distribution of interpersonal skills is spread out; 60% of VET workers have acquiredat most one interpersonal skill. Yet, a considerable fraction has acquired three or even fiveinterpersonal skills (15% each). In comparison, the distributions of cognitive and manualskills are smoother. Most workers have acquired one (29%), two (32%) or three (21%)cognitive skills. Finally, more than 95% of all workers have acquired two or fewer manualskills, with a peak at two skills (38%).

Table 1 (right panel) also provides some insight into how the three skill dimensions arerelated. The two negative correlation coefficients with manual skills indicate that workersspecialise by either acquiring manual or non-manual (interpersonal/cognitive) skills. Thesupply of interpersonal and cognitive skills, instead, correlates positively. Workers withhigh (low) interpersonal skills tend to have high (low) cognitive skills.

Figure 1 further visualises the different skill bundles (or combinations) supplied bythe workers in our sample. It displays the joint distribution of cognitive and interpersonalskills for each of the four different values of manual skills.

Figure 1: Skill bundles supplied by workers

Skill bundles differ greatly by frequency. Some skill bundles make up 5% or more ofthe sample, for other skill bundles we do not have a single observation. Generally, skill

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bundles close to the horizontal 00-55 line (0 interpersonal-0 cognitive to 5 interpersonal-5cognitive) are somewhat more frequent than those off this line, reflecting the positive cor-relation of these skills. Moreover, workers with relatively high manual skills have onlyfew interpersonal and cognitive skills, and vice versa.

Given the range of each skill dimension, there are 6 × 6 × 4 = 144 possible skillcombinations. Effectively, we observe only 45 of them in our sample. For the subsequentdescriptive analysis and estimation of the model in Section 4.2, we regroup workers intooccupational clusters based on the skills they acquired during VET. To do this, we firstdivide each of the three skill dimensions into groups of roughly equal size. We distinguishlow (0), medium (1,2) and high (3 and above) interpersonal skills; low (0,1), medium(2) and high (3 and above) cognitive skills, and low (0,1) and high (2,3) manual skills.There are 18 (3× 3× 2) possible occupation clusters, but two remain empty without anyobservation.

2.3.2 Labour market outcomes

The skill bundle acquired in VET is a key determinant of labour market outcomes. Figure2 illustrates this point by plotting hourly wages (left panel) and unemployment rates (rightpanel) of Swiss workers with a VET degree for different levels (black, grey and light-greybars) of the three skill dimensions. For comparison purposes, the figure also depicts therespective hourly wages and unemployment rates of workers with completed compulsoryeducation (dashed line) and those with general upper secondary education (black line) astheir highest education level.

Figure 2: Hourly wages and unemployment rates by skill dimensions

Occupations with high cognitive skills are characterised by higher hourly wages (by 4Swiss francs) and slightly lower unemployment rates (by 0.5pp) than occupations withlow cognitive skills. Occupations with high interpersonal skills are characterised byhigher hourly wages (by 3 Swiss francs), but also higher unemployment rates (by more

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than 1pp) than those with low interpersonal skills. Finally, more manual skills are notassociated with higher hourly wages (if anything, they are slightly lower). However, theunemployment rate is around 1pp lower for workers with high manual skills than forworkers with low manual skills.

Figure 2 also offers some insight into how VET workers fare compared to workerswho have only completed compulsory education (9 years) and to workers who have com-pleted general upper secondary education (12 to 13 years). Average hourly wages of VETworkers generally lie between these two comparison groups. Only VET workers withhigh cognitive skills earn hourly wages comparable to those of workers with general up-per secondary education. VET workers seem not to primarily benefit from their trainingin terms of higher wages, but rather in terms of lower unemployment rates. Unemploy-ment rates of VET workers are substantially lower than the unemployment rates of bothworkers with compulsory education (5.3%) and with general upper secondary education(6.7%).

Given the correlation of the three skill dimensions, we provide some further descrip-tive evidence on labour market outcomes. Table 2 shows descriptive statistics by occu-pational clusters, Table 3 presents reduced form regressions of (log) hourly wages andunemployment on interpersonal, cognitive and manual skills. The three panels in Table 2relate to high (H), medium (M) and low (L) interpersonal skills, respectively. Within eachpanel, the upper part (3 lines) refers to high and the lower part (3 lines) to low manualskills. Finally, within each interpersonal-manual skill group cognitive skills go from highto medium to low.

Average hourly wages of VET workers differ substantially across occupational clus-ters, but they are generally above those of workers with only compulsory education. MostVET workers with high cognitive skills have average hourly wages of 39 Swiss francsand more, exceeding the average hourly wage of workers with general upper secondaryeducation. Table 3 shows that returns to all three skills appear positive, even after con-trolling for age. Returns to interpersonal and cognitive skills are in a similar range, whilereturns to manual skills are somewhat smaller. The negative interaction terms betweenskills could indicate a substitutability of these skills.

We also observe important differences in hourly wages within each cluster. Part of thewithin-cluster variation reflects differences in the exact number of skills, part of it stemsfrom differences in age, experience, region, industry and other factors within clusters (notshown). Having more interpersonal or cognitive skills is also associated with a (slightly)

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Table 2: DESCRIPTIVE STATISTICS BY OCCUPATIONAL CLUSTERS

Obs unemp hourly wages agemean std. dev.

H-interpersonal

H-cognitive 0 n.a. n.a. n.a. n.a.H-manual M-cognitive 0 n.a. n.a. n.a. n.a.

L-cognitive 1,244 0.039 37.67 10.64 40.52

H-cognitive 2,042 0.047 40.14 15.43 39.05L-manual M-cognitive 1,052 0.030 33.89 9.91 39.47

L-cognitive 255 0.082 29.62 6.52 39.29

M-interpersonal

H-cognitive 1,094 0.018 40.09 10.74 44.46H-manual M-cognitive 456 0.024 38.06 12.87 41.49

L-cognitive 446 0.027 33.73 9.77 41.78

H-cognitive 940 0.040 39.13 11.88 42.20L-manual M-cognitive 1,028 0.040 35.89 9.07 41.82

L-cognitive 1,801 0.048 36.09 11.22 39.36

L-interpersonal

H-cognitive 299 0.033 33.74 7.86 40.51H-manual M-cognitive 1,467 0.033 33.41 7.78 39.33

L-cognitive 607 0.035 33.84 10.33 40.99

H-cognitive 147 0.020 40.51 11.21 43.99L-manual M-cognitive 489 0.022 33.82 8.85 42.98

L-cognitive 367 0.025 34.17 8.44 41.73

all clusters 13,734 0.037 36.55 11.39 40.70

Comparison with lower and next higher educational achievement

Compulsory schooling 3,845 0.053 31.29 15.97 42.65General upper secondary education 1,161 0.067 38.98 27.73 38.43

Notes: H-interpersonal stands for high (3 and more), M-interpersonal for medium (1 or 2),and L-interpersonal for low (none) interpersonal skills. H-cognitive stands for high (3 andmore), M-cognitive for medium (2) and L-cognitive for low (none or one) cognitive skills.H-manual stands for high (2 or 3) and L-manual for low (none or one) manual skills.

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Table 3: REDUCED-FORM ESTIMATES.Log hourly wages Unemployment

Interpersonal skills 0.0497 *** 0.0029 **(0.0041) (0.0011)

Cognitive skills 0.0511 *** -0.0017(0.0053) (0.0014)

Manual skills 0.0337 *** -0.0020(0.0075) (0.0022)

Interpersonal*cognitive -0.0106 ***(0.0011)

Interpersonal*manual -0.0115 ***(0.0018)

Cognitive*manual -0.0169 ***(0.0032)

Age 0.0430 *** -0.0057 ***(0.0014) (0.0011)

Age squared -0.0004 *** 0.0001 ***(1.76×10−5) (1.35×10−5)

Constant 2.3833 *** 0.1503 ***(0.0303) (0.0237)

R2 0.2254 0.0034Observations 11,960 13,734

Notes: The left-hand column, in which log hourly wages is the dependentvariable shows least-squares estimates. The right-hand column, in which adummy indicator for unemployment is the dependent variable, shows esti-mates from a linear probability model. Robust standard errors are in paren-theses. *** p < 0.01, ** p < 0.05, * p < 0.1.

higher standard deviation of hourly wages.

VET workers in all occupational clusters have lower unemployment rates than work-ers without VET (independent of their level of education).9 Unemployment rates varyacross occupational clusters, but these differences appear to be less systematic than forhourly wages.10 Table 3 indicates that having more interpersonal skills is associated with

9An exception presents the occupational cluster with high interpersonal, low manual and low cognitive skillsfor which the unemployment rate exceeds 8% and hourly wages are around 29 Swiss Francs. This is thesecond smallest group in our sample and hence, the unemployment rate is less precisely measured than forthe other occupational clusters.

10Note that all observed differences in unemployment rates of VET workers across occupational clusters mustbe the result of differences in labour market transitions after graduation, as all VET workers were employed

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a slightly higher risk of unemployment, while cognitive and manual skills do not have asignificant effect. Appendix C presents further descriptive evidence on employment andunemployment transitions by occupational cluster.

We know from standard economic theory, however, that wages and unemployment arejointly determined. The previous analysis is thus purely descriptive. To understand theresulting wages and unemployment rates in different occupational clusters, we need tostudy how supply and demand for different skills interact and how they determine theseequilibrium outcomes. To do so, we present a simple search and matching model withoccupational skills in the next section.

3 A simple matching model with occupational skills

To study the role of occupational skills in wages and employment dynamics, we present asimple general equilibrium search and matching model in the spirit of Pissarides-Mortensen-Diamond (see Pissarides, 2000). Workers are heterogeneous. They are characterised bya set of skills which differ along several dimensions. Firms use these skills in differentcombinations to produce an output.

Our model is in continuous time and features infinitely lived agents who discount timeat rate r. We assume that search is random and that jobs get exogenously destroyed. Keyingredients of our simple model are the multidimensional skill supply by workers andthe multidimensional demand for skills by firms. Workers are heterogeneous in that theyacquired different skills during their vocational education and training. Each worker pos-sesses an occupation-specific (time-invariant and multidimensional) skill bundle denotedby x. Each element of x is non-negative. Firms, on the other hand, differ in their demandfor these skills. Their demand for a specific skill bundle is denoted by skill weights α.

Under random search, an unemployed worker with skill bundle x gets an unemploy-ment flow of b and meets a firm at some constant rate λ. An employed worker receiveswage w and faces (exogenous) job destruction at rate η. The wage is a function of theworker’s skill bundle x, firms’ skill weights α, and the resulting match productivity p.For simplicity, we assume that there is no on-the-job-search. The value functions of the

during their training.

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worker’s problem are given by:

rVU(x) = b(x) + λEw max [VE(w, x)− VU(x), 0] (1)

rVE(w, x) = w + η [VU(x)− VE(w, x)] , (2)

where r is the instantaneous discount rate, VU is the value of unemployment, and VE isthe value of employment. Ew denotes the expectation operator with respect to wages w.

A firm’s value of a filled job depends on the productivity of the match p and the wagew which the firm needs to pay. Whenever a firm and a worker meet, the potential pro-ductivity of this match is assumed to be p = α′x (following Flinn and Mullins, 2015). αis a skill weighting vector which is independently and identically distributed according tothe multivariate distribution function G(α). Each component of α is restricted to be non-negative.11 A filled job gets destroyed at rate η. We assume that there is no endogenousvacancy creation.12 The value of a filled job between a worker with skill bundle x and afirm with a skill weighting vector α is given by:

rVF (w, α) = α′x− w + η [VF (w, α)] . (3)

The worker and the firm engage in Nash-bargaining over the wage w by solving thefollowing bargaining problem:

maxw

[VE(w, x)− VU(x)]β [VF (w, α)]1−β , (4)

where β is the worker’s bargaining power. Using Equations (2) and (3), we can rewritethe Nash-bargaining problem and derive the following wage equation:

w(α, x) = βα′x+ (1− β)rVU(x). (5)

Let us define the set of reservation skills α∗(x). It is the set of acceptable weightingvectors for which a worker with skills x is indifferent between employment and unem-ployment. Moreover, the reservation skills also pin down the reservation wage w∗(x):

w(α∗(x), x) = βα∗(x)′x+ (1− β)rVU(x) = rVU(x) (6)

w∗(x) = α∗(x)′x = rVU(x). (7)

11This assumption implies that there are no (direct) costs for the firm when hiring a worker who has skillswhich are not needed by the firm.

12It is straightforward to extend the model to endogenous vacancy creation. Under the common free entrycondition, the value of an unfilled vacancy is equal to 0 and the value of a filled job is the same as in oursetting.

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We now turn to the rate of a match being formed. It is the product of the offer rate λand the probability of the firm’s skill weights α lying within or above the set of reservationskills. The rate of forming a match for a worker with skill bundle x is given by:

h(x) = λ

∫α∗(x)

dG(α). (8)

In a steady-state equilibrium, the inflow into and the outflow from unemploymentneed to be equal. This gives rise to the following equation, from which we can derive thelikelihood of finding a worker with skills x in unemployment:

[1− u(x)] η = u(x)h(x) (9)

u(x) =η

η + h(x). (10)

Differences in unemployment rates across skill bundles x are thus driven by differ-ences in the rate of accepting job offers (and not by differences in job destruction rates).

Despite its simplicity, the model has several appealing features. It allows us to jointlymodel (un-)employment and wages, which differ across skill bundles. Two key elementsof the model are the demand for skills by firms G(α) and the flow cost of unemploymentfor different skill bundles by the worker b(x). Together they determine the set of reserva-tion productivities α∗(x) for which the worker and firm are indifferent between forminga match or not. The reservation productivity impacts the arrival rate of acceptable job of-fers and hence, unemployment dynamics (see Equation (8)), and wages (see Equation (5)).

4 Structural estimation

4.1 Parametric assumptions and functional forms

In this section we describe how we take the previously described model to the data. First,we presume the labour market to be in the steady state. Second, we make some parametricassumptions about the skill demand distribution G(α) and the flow cost of unemploymentb(x). More specifically, we assume that the productivity of the match is given by thefollowing equation,

p = α′x = α0 + αIxI + αCxC + αMxM , (11)

where α0 is a general productivity shock, and αI , αC and αM are the demand for interper-sonal, cognitive and manual skills, respectively. We assume that α0 is independently andidentically distributed according to a log-normal distribution with location µ0 and scale

15

σ0. Whenever a worker and a firm meet, they draw a new general productivity shockα0. Moreover, the general productivity shock is assumed to be independent of the skill-specific demands (and the skill supply). The skill-specific demands αj with j = I, C,M

are assumed to be distributed according to a Gaussian copula with log-normal marginalswith location µj and scale σj . The correlation between two skill-specific demands i and jis given by ρij .

This parametrisation of the productivity is at the same time parsimonious and flexi-ble. It imposes worker-job complementarity, for which evidence presented in Lindenlaub(2017) provides support. This specific parametrisation allows for different mean and vari-ation in returns to each skill dimension. Moreover, the Gaussian copula renders it possiblefor the different skills to be positively or negatively correlated. A positive correlation indi-cates complementarity in the demand for skills, a negative correlation between two skillsindicates that firms prefer specialists.

We also impose some structure on the flow cost of unemployment b(x). We opt forthe following parsimonious structure:

b(x) = b0 + bIxI + bCxC + bMxM , (12)

where b0 is the general flow cost of unemployment common to all workers (i.e. we expectb0 to be negative), and bj the marginal cost (or value) of unemployment of skill j. If bj isnegative, having more skills j makes being in unemployment more costly (for example,because of skill depreciation), while the converse is true if bj is positive.

4.2 Estimation method and identification

We estimate the model by using the Method of Simulated Moments (MSM) as in Flinnand Mullins (2015). Table 4 gives an overview over all parameters of the model andwhich moments are used for their identification. There are 19 parameters in total, but twoparameters are calibrated outside the model. The remaining 17 parameters are identifiedby moments from the data. Notice that we directly observe the workers’ skill bundle x,which simplifies the identification of the model substantially. To reduce the number ofmoments and increase the number of observations for each moment, we regroup workerswith different skill bundles x into the 16 occupational clusters outlined in Section 2.3.1.

Identification of many parameters of the model is achieved by exploiting differencesin mean hourly wages, the standard deviation of hourly wages, the first percentile ofhourly wages, unemployment rates, and UE- and EU-labour market transition rates be-tween occupational groups. Let us suppose we knew reservation wages w∗(x) and take

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Table 4: Model parameters and corresponding momentsParameter Moment #

Productivity and skill-specific demands (log-normal marginals)

General productivity: µ0, σ0 Mean & standard deviation of hourly wagesby occupation cluster 32

Interpersonal skills: µI , σI same as aboveCognitive skills: µC , σC same as aboveManual skills: µM , σM same as aboveCorrelations: ρIC , ρIM , ρCM same as above

Flow cost of unemployment

Common flow cost: b0 First percentile of hourly wagesby occupation cluster 16

Interpersonal skills cost: bI same as aboveCognitive skills cost: bC same as aboveManual skills cost: bM same as above

Offer arrival and destruction rates

Offer arrival rate: λ Yearly UE-transition rates by occupation cluster 16Destruction rate: η Yearly EU-transition rates by occupation cluster 16

Unemployment rates by occupation cluster 16

Calibrated parameters

Bargaining power worker: β = 0.67 Siegenthaler and Stucki (2015)Interest rate: r = 0.05

Total moments 96

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the parametric assumptions about the match productivity p = α′x in Equation (11) andthe calibrated value of the labour share β as given. Hence, we know that the produc-tivity distribution matches one-to-one into the wage distribution given in Equation (5).Differences in mean hourly wages and in standard deviation of hourly wages across occu-pational groups allow us to pin down the eleven parameters of the match productivity (i.e.the demand for each skill, the correlation of these skills, and the general productivity).Mean hourly wages and the standard deviation of hourly wages are 32 moments.

We use the first percentile of hourly wages in each occupational cluster to identify thereservation wages w∗(x). Together with the productivity-related parameters (identifiedabove), they allow us to identify the common and skill-specific costs of unemployment.These are another 16 moments.

To identify the job arrival rate λ and the job destruction rate η, we rely on year-to-year unemployment-to-employment (UE) transitions, employment-to-unemployment(EU) transitions and unemployment rates by occupational clusters. In fact, given that weassume constant (i.e. skill-independent) job arrival and job destruction rates, it would suf-fice to use overall UE- and EU-transitions rather than by occupational cluster. However,these additional moments also help us to pin down the reservation productivities α∗(x)

(and hence, reservation wages) and the parameters of the match productivity distributionG(α). In total, we have 48 moments related to labour market transitions.

Following Flinn (2006), we use information from outside the sample on firms’ capitalshare to identify the firm’s surplus. We set β to 0.67.13 Finally, we fix the interest rate rat 5%.

Combining all this, we set up the following MSM estimator

ωN,WN= arg min

ω∈Ω

(MN − M(ω)

)′WN

(MN − M(ω)

), (13)

where ω is a parameter vector and Ω is the parameter space. The parameter vector con-tains the general productivity location parameter µ0 and scale parameter σ0, the skill-demand location µj and scale parameters σj (in total, 6 parameters), the correlation ofskill-demands ρij (3 parameters), the common and skill-specific flow costs of unemploy-ment b0, bj , as well as the offer arrival rate λ and the job destruction rate η. The parameter

13The labour share, which is often used as a proxy for workers’ bargaining power, has traditionally beenthought to be constant at around two thirds (see Kaldor, 1957). While Karabarbounis and Neiman (2014)observe that the labour share has been declining to around 60 percent in the United States and many othercountries since around 1980, Switzerland appears to be an exception, where it has actually remained ataround 67 percent (see Siegenthaler and Stucki, 2015).

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space corresponds to the real numbers for the location parameters µ0, µj and the flowcosts of unemployment b0, βj , to positive real numbers for the scale parameters σ0, σj ,the offer arrival rate λ and the destruction rate η, and to real numbers between -1 and 1for the correlation coefficients. Furthermore, we restrict the parameter space of the cor-relation coefficients to ensure that the resulting symmetric correlation matrix is positivesemi-definite. WN is a diagonal matrix with elements equal to the inverse of the (squared)standard error of the corresponding observed moment MN . The standard errors for theobserved mean hourly wages, unemployment rates, UE- and EU-transition rates are esti-mated from the sample moments, the standard errors of the standard deviations and thefirst percentile of hourly wages were bootstrapped using 1,000 replications.

4.3 Simulation procedure

To perform our estimation using MSM, we need to compute the simulated counterpart ofthe observed moments described in Table 4 used to evaluate Equation (13). Our targetmoments include the mean, standard deviation and first percentile of hourly wages byoccupational cluster, unemployment rates by occupational cluster, as well as the cluster-specific EU- and UE-transition rates. To do so, we assume the labour market to be insteady state and produce a simulated data set with 20 replicas of each worker in our ob-served data set (i.e. there are 20 ∗ 5, 050 = 101, 000 simulated workers). These simulatedworkers have (approximately) the same skill distribution x as the observed sample. Foreach worker we simulate five consecutive labour market spells (i.e. employment and un-employment spells). Our simulation protocol consists of the following steps:

1. For each worker in the simulated data set, we first determine his skill bundle x. Wekeep the skill bundle constant across all iterations.

2. At the beginning of each new iteration, we first compute the reservation wage foreach skill bundle x. To do this, we need to find the fixed point of Equation (1) foreach x.14

3. Once the reservation wage w∗(x) is known, we can simulate the labour market stateand wage (if any) in the first spell. For this purpose we draw a productivity shockα, which results in a potential wage w(x, α). If the resulting wage is below thereservation wage, the worker is unemployed in the first spell. Among those workers

14To find the fixed point, we first rearrange Equation 2 and substitute it into Equation (1). We then (nu-merically) evaluate the right-hand-side of Equation (1) (i.e. the expected maximum of the employmentsurplus and 0) by drawing 50 productivity shocks α and computing the average sample maximum of theemployment surplus and 0.

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with a resulting wage equal or above the reservation wage, there is a share κ(x) whois unemployed in the first spell.15 The remaining workers are employed in the firstspell and get wage w(x, α).

4. We then simulate the duration of the first spell of each worker. For those who areemployed, we draw the duration of their employment spell from an exponentialdistribution with destruction rate η. Unemployed workers receive a wage offer (de-termined by the draw of a productivity shock α) after a duration which is drawnfrom an exponential distribution with offer arrival rate λ. If the wage offer is abovethe reservation wage, the worker accepts and becomes employed. Otherwise hecontinues his search and receives a next wage offer according to the same rules asdescribed for the first offer. He searches until he receives an acceptable wage offer.

5. We repeat steps 2) to 4) to simulate also the data for the second to the fifth labourmarket spell (with κ = 0). Using the information on the employment status at thebeginning of the first spell, the wage and the employment status after one year (usingthe data on the duration of each spell), we can compute the simulated moments.

Finally, we iterate this process (steps 2) to 5)) for different values of ω using a Nelder-Mead simplex algorithm until the minimum of the loss function is found.

5 Results

5.1 Estimated parameters

Table 5 presents point estimates and asymptotic standard errors of the model parameters.In the upper panel (in columns 4 and 5) we also show the (untruncated) mean and stan-dard deviation of the general productivity and skill demand distributions. These numbersare more readily interpretable than the location and scale parameters of the log-normaldistribution.16

The log-normal general productivity distribution has a mean of 40.36 CHF and a stan-dard deviation of 13.14 CHF. The general productivity α0 captures all variation in pro-ductivity which is not related to the demand and supply of interpersonal, cognitive and

15This ensures that the unemployment rate at the beginning of the first spell equals the expression in Equation(10). κ(x) equals η−(1−p(x))(η+λp(x))

p(x)(η+λp(x)) , where p(x) is the fraction of those who have a potential wage equalor above the reservation wage.

16Notice that the mean of a log-normally distributed random variable is equal to exp(µ + σ2/2), and thevariance is given by

[exp(σ2)− 1

]exp(2µ+ σ2).

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Table 5: ESTIMATED PARAMETERS

Productivity

Estimate Std. Err. Mean Std dev.

µ0: General productivity (location) 3.647 0.099 40.335 13.142σ0: General productivity (scale) 0.318 0.030

µI : Interpersonal skills (location) -0.261 0.761 1.288 1.727σI : Interpersonal skills (scale) 1.014 0.342µC : Cognitive skills (location) 0.527 0.373 2.245 1.954σC : Cognitive skills (scale) 0.750 0.164µM : Manual skills (location) 0.025 1.960 1.329 1.096σM : Manual skills (scale) 0.720 1.122

ρIC : Interpersonal-cognitive correlation 0.937 0.071ρIM : Interpersonal-manual correlation -0.319 0.542ρCM : Cognitive-manual correlation -0.088 0.553

Offer and destruction rates

λ: Offer arrival rate 1.065 0.007η: Destruction rate 0.034 0.003

Unemployment cost

b0: General unemployment cost -174.995 96.799bI : Marginal cost interpersonal skills -23.104 14.075bC : Marginal cost cognitive skills -30.765 15.530bM : Marginal cost manual skills -34.864 43.592

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manual skills. It includes the effect of age, experience, tenure, industry, and region, aswell as the impact of unobserved idiosyncratic factors.

The demand for (and returns to) cognitive skills is highest, followed by manual andinterpersonal skills. The mean productivity of cognitive skills is estimated at 2.25 CHFwith a standard deviation of 1.95 CHF. Although the mean productivity for manual andinterpersonal skills is very similar at 1.33 CHF and 1.29 CHF, respectively, the demandfor interpersonal skills is more dispersed (with a standard deviation of 1.73 CHF). Somefirms demand high interpersonal skills (and remunerate them accordingly), while otherfirms do not need and remunerate interpersonal skills. In contrast, the demand for manualskills is more compressed with a standard deviation of 1.10 CHF.

We find evidence of strong complementarity in the demand for interpersonal and cog-nitive skills, with a correlation coefficient of 0.94. The correlation of the demand forthese two skills with manual skills is negative, albeit not significant, indicating that firmsrequire workers specialised either in manual or non-manual skills.

Despite a different context, model and sample, our estimates on the productivity distri-butions compare well with the production function estimates reported by Lise and Postel-Vinay (2016) for the US. In particular, our estimates suggest the same order (and relativemagnitude) in productivity, that is, cognitive skills clearly dominate manual and interper-sonal skills. Moreover, we also find complementarity between interpersonal and cognitiveskills (our correlation coefficient is somewhat higher), and a negative correlation betweeninterpersonal and manual skills.

In terms of job creation and destruction dynamics, we estimate that unemployed work-ers get on average 1.07 job offers over a year, while 3.4% of filled jobs get destroyed overthe same time.

Finally, our estimates indicate that the cost of being in unemployment increases withall three skills, possibly reflecting the cost of skill depreciation while unemployed. Themarginal cost of unemployment is lowest for interpersonal skills and highest for manualskills.17 However, these costs are not very precisely estimated.18

17If the marginal cost of unemployment by skill is interpreted as the cost of skill depreciation, our resultsreflect the same pattern as the speed (and cost) of skill accumulation and depreciation found by Lise andPostel-Vinay (2016).

18Note that none of the parameters related to manual skills are precisely estimated. Given that the skill supplyof workers is very skewed towards few manual skills, it appears that these parameters are not well identifiedand therefore, not precisely estimated.

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5.2 The supply and demand for skills

The productivity of a match is determined by the skills supplied, i.e. the skill bundle x aworker is endowed with, and by a firm’s demand for these skills α. Our parametric speci-fication of the productivity as p = α′x implies worker-job complementarity. This entailsthat productivity is highest if the worker supplies the skills which are in high demand bythe firm.

Figure 3 depicts the marginal probability density function (left panel) and the cumu-lative distribution function (right panel) for the estimated demand of interpersonal (dottedlines), cognitive (black lines) and manual skills (dashed lines).

Figure 3: Marginal probability density function and cumulative distribution function forthe demand of interpersonal, cognitive and manual skills

Table 5 showed that the mean productivity is equal to 1.29 CHF for interpersonal, 2.25CHF for cognitive and 1.33 CHF per hour for manual skills, respectively. However, thesereturns vary substantially with the relative position of the firm in the demand for theseskills. Let us suppose that the worker meets a firm with a high demand for a certain skill,i.e. at the top 5% of the distribution. As shown in Figure 3 (right panel), the productivityof an additional unit of skill at the upper end amounts to 4.08 CHF per hour for interper-sonal, 5.82 for cognitive and 3.35 for manual skills, respectively. The large dispersion inthe demand for interpersonal and cognitive skills might make waiting for a better offermore attractive (ceteris paribus) for workers with high levels of these skills.

This simple analysis ignores that the demand for different skills is correlated. Figure4 thus plots the joint distribution of the demand for cognitive-interpersonal (left panel),manual-interpersonal (middle panel) and cognitive-manual (right panel) skills.19

19Notice that the demands in thes histogrammes are truncated at a productivity of 6 CHF. All higher produc-tivity realisations are regrouped in the highest category of the histogrammes.

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Figure 4: Joint sampling density for the demand of interpersonal, cognitive and manualskills

Figure 4 (left panel) illustrates well the strong positive correlation between the de-mand for interpersonal and cognitive skills, with a high density along the 00-66 diagonal.The middle and right panel show the (weaker) negative correlation between the demandfor manual skills and interpersonal/cognitive skills. In this case, we observe a somewhathigher frequency along the 06-60 line.

Generally, our results suggest that the skill supply is well aligned (though not per-fectly) with the demand for skills. The demand for cognitive skills is highest, with anaverage productivity of 2.25 CHF. As shown in Table 1, workers have acquired on av-erage more cognitive skills (2.14) than interpersonal and manual skills (1.81 and 1.23,respectively). The alignment also holds true for skill bundles. Firms demand a highcomplementarity of cognitive and interpersonal skills (correlation of 0.94), and workerswith high cognitive skills also tend to have high interpersonal skills (correlation of 0.33).Moreover, firms have a slight preference for either manual or non-manual specialists (i.e.with a manual-interpersonal skill demand correlation of -0.32 and manual-cognitive cor-relation of -0.09). At the same time, workers also show a tendency to either specialisein manual or non-manual skills (with a manual-interpersonal correlation of -0.46 and amanual-cognitive correlation of -0.26).

The effect of this complementarity in the demand for skills can also be illustrated asfollows: Let us suppose a worker has to decide whether to train in an occupation special-ising in manual or interpersonal skills. If the worker acquires five skills, he would get onaverage a post-VET wage of 34.37 CHF per hour if he specialises in manual, and 34.76CHF per hour if he specialises in interpersonal skills, respectively. What would happen ifthe worker did not fully specialise, but if he acquired three manual or interpersonal skills

24

in combination with two cognitive skills? His average hourly wage would be 34.46 CHFfor the manual-cognitive skill bundle, and 35.89 CHF for the interpersonal-cognitive skillbundle. There is a wage difference of 4% between two different skill bundles with thesame number of skills, but one is highly demanded (i.e. interpersonal-cognitive) whilethe other is not (i.e. manual-cognitive). Note that replacing two (relatively lowly remu-nerated) manual skills against two (highly remunerated) cognitive skills results in almostno wage increase, because firms do not value manual-cognitive skill combinations butprefer manual or non-manual specialists.

5.3 Goodness of fit

Tables D.1 and D.2 in Appendix D display how well our model is able to match thecluster-specific moments observed in the data.

A comparison of observed and simulated moments shows that the model generallyperforms well at replicating both the moments related to hourly wages (mean, standarddeviation and first percentile), as well as the unemployment rates, and the moments relatedto transitions into and out of unemployment by cluster. The model slightly underpredictsthe overall mean hourly wage at 35.84 CHF (36.55 CHF observed), but it closely fits theoverall standard deviation of hourly wages at 10.23 CHF (10.82 CHF observed) and theoverall first percentile of hourly wages at 18.91 CHF (18.94 CHF observed). In terms ofunemployment, our model produces a slightly lower overall unemployment rate (3.25%)than the one observed in the data (3.7%), the main reason being that the model overpre-dicts the overall job-finding rates (65% simulated compared to 59% observed) while thejob destruction rates are on average precisely matched (2.1% simulated, 2.2% observed).

While the fit of the model in the overall mean of the targeted moments is reasonablygood, it does not generate the same degree of variation across occupational clusters in themean hourly wages that we observe in the data. In particular, the model generally pro-duces too low hourly wages for occupation clusters with high cognitive skills. In terms ofunemployment, the observed cluster-specific unemployment rates do not follow a system-atic linear pattern and they are imprecisely measured in the observed data (i.e. relativelylarge standard errors). Hence, it cannot come as a surprise that the model does not matchthem particularly well. The feature of increasing unemployment rates with interpersonalskills (see the reduced form results in Table 3) is only weakly reproduced by our model:The weighted unemployment rate is 3.28% for those with high interpersonal skills (4.29%observed) and 3.17% for those with low interpersonal skills (3.05% observed).

In fact, the model does not only explain the cluster-specific means and standard devi-

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Figure 5: Goodness of fit: Wage distributions of observed (blue) and simulated (orange)wages by occupation cluster

ations of hourly wages, but it does also a good job at matching almost all cluster-specificwage distributions as shown in Figure 5. In addition, the good fit of the wage distributionsvalidates our parametric assumption of log-normality of the general productivity as wellas of the skill-specific demands.

There is, however, one cluster, for which our model performs badly in most respects.This concerns the high-interpersonal-low-manual-low-cognitive cluster in line 6 in Ta-ble D.1. This occupation cluster counts relatively few observations and appears to be anoutlier. It has by far the lowest mean hourly wage (almost 4 CHF lower than all otherclusters), the lowest standard deviation in hourly wages and the highest unemploymentrate at 8.2%. Our model fails to replicate these patterns and overpredicts the mean andthe standard deviation of hourly wages (see also Figure 5). Moreover, the model clearlyunderpredicts the unemployment rate.

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6 The value of VET

6.1 The returns to VET skills

To quantify the value of the skills acquired in VET, we compare average wages, unem-ployment rates, unemployment duration, and annual earnings in two different scenarios inTable 6.20

The baseline scenario (VET with skills) presents these outcomes for workers whohave obtained a VET degree and who have acquired interpersonal, cognitive and/or man-ual skills. It corresponds to our estimated specification from Section 5. In the secondscenario (VET without skills), we simulate the outcomes of the same workers with a VETdegree, but assuming that the skills acquired in VET are worthless. That is, we assumethat skills neither impact productivity nor the cost of unemployment. Moreover, we as-sume that VET workers without skills would still face the same job offer and destructionrates.

Table 6: VALUE OF VET SKILLS: WAGES, UNEMPLOYMENT AND EARNINGS

VET VETwith skills without skills

(estimation) (simulation)

Avg. productivity (in CHF) 49.1 40.5Avg. hourly wage (in CHF) 35.8 32.81st percentile hourly wage (in CHF) 18.8 18.9Unemployment rate 3.3% 3.3%

Avg. annual earnings (in CHF) 70,794 64,806

Comparing these two scenarios, we find that the skills acquired in VET translate onaverage into an hourly wage increase of 3 Swiss Francs. This wage increase is solely de-rived from the skills acquired during VET and not from obtaining the VET degree. Hence,the returns to the skills of a 3-year or 4-year VET degree amount to around 9.1%.21 Thesereturns are of a similar magnitude as the returns to a year of schooling on wages of around10% reported in the literature (Card, 1999). Notice that we calculate returns to VET only

20Average hourly wages, the first percentile of hourly wages and unemployment rates are computed fromthe simulated model. Unemployment duration is calculated as 1

h , where h is the average estimated rate ofaccepted offers. Annual earnings are obtained as the product of annual earnings when employed (assuming2,040 working hours a year) and the employment share.

21Note that apprentices studying for a VET degree spend around one third of their time in school and twothirds working in their training firm.

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for those who obtain a VET degree but do not continue their training further. Overallreturns to VET might be larger given that some workers with a VET degree (who are notin our sample) go on to study for a tertiary degree and earn even higher wages.

However, occupational skills not only affect productivity (and hence, hourly wages),but they also have an impact on the probability of unemployment. We find that VET work-ers without skills would not see their unemployment rate rise compared to VET workerswith skills. This result is due to occupational skills impacting reservation wages (andhence, unemployment rates) through two opposed channels. First, skills increase the ex-pected value of matches and, as such, translate into higher reservation wages. Second, weestimate that being in unemployment is more costly with more skills - possibly because ofskill depreciation - and hence, having more skills lowers reservation wages. In our currentsetting, these two forces almost cancel out and leave unemployment rates unaffected. Asa consequence, the difference in annual earnings between VET workers with and withoutskills also amounts to 9.2%.

6.2 The value of VET for those with low abilities

Returns to VET skills differ across workers in different occupational skill groups. Moreo-ever, workers who only completed compulsory education might benefit substantially fromobtaining a VET degree and the skills it confers. To evaluate the value of a VET degreefor these workers, we estimate a simple search model for workers with compulsory edu-cation (but nothing more). Table E.1 in Appendix E reports the estimated parameters ofthis simple search model for workers with only compulsory education. In this simplifiedmodel all parameters related to skills are dropped.

In Table 7 we compare labour market outcomes such as hourly wages, annual earnings,unemployment rates and welfare of these workers with the respective outcomes of work-ers with VET. In order to account for selection into different occupational skill groups inVET, we limit our comparison to two occupational skill groups in which workers have onaverage similarly low cognitive abilities and comparable personality traits.22 These arethe occupational cluster with intermediate interpersonal, intermediate cognitive and lowmanual skills (i.e. cluster 11) and the cluster with high manual, intermediate cognitiveand low interpersonal skills (i.e. cluster 14). Outcomes of workers with compulsory edu-cation are shown in column 2, while the corresponding outcomes of workers in clusters 11and 14 are given in columns 3 to 6, respectively. Columns 3 and 5 present the estimated

22See Table A.1 in Appendix A for details on cognitive abilities (PISA math and reading scores) and self-assessed personality traits (persistence, locus of control, ambition) of workers in different educational tracksand occupational skill clusters.

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results for VET workers with a VET degree and VET skills, while columns 4 and 6 relateto the simulations results for VET workers without skills. The difference between thesetwo scenarios allows us to disentangle the effect of the VET degree versus VET skills.

Table 7: VALUE OF VET FOR LOW-ABILITY WORKERS: WAGES, UNEMPLOYMENT, EARNINGS

AND WELFARE

no VET VET VETcluster 11 cluster 14

with skills without with skills without(estimation) (estimation) (simulation) (estimation) (simulation)

Avg. productivity (in CHF) 47.0 47.6 40.4 47.7 40.4Avg. hourly wage (in CHF) 31.5 35.5 32.9 35.1 32.81st percentile wage (in CHF) 14.8 19.3 18.8 19.2 18.8Unemployment rate 6.5% 3.3% 3.3% 3.4% 3.4%

Avg. annual earnings (in CHF) 60,011 70,048 64,831 69,139 64,726

Job destruction rate (per year) 0.058 0.034 0.034Job offer rate (per year) 0.84 1.06 1.06

Value of unemployment 0 10.91 9.39Value of employment 14.51 21.79 20.75Avg. welfare 13.57 21.44 20.33

We find that returns to VET (degree and skills) in hourly wages would amount to11.5% (in cluster 14) and 12.8% (in cluster 11) for those with compulsory education.4.4pp of this effect can be attributed to the return to the VET degree without skills (com-paring columns 4 and 6 with column 2), while the remaining returns can be attributedto VET skills. In addition to lower hourly wages, workers with only compulsory educa-tion also have a risk of unemployment which is almost twice as high as their similarlyable peers with a VET degree in clusters 11 and 14 (6.5% versus 3.4%). Altogether, thisresults in 13% to 14% lower annual earnings for workers without a VET degree and skills.

The lower part of Table 7 offers valuable insights into how these large differencesemerge. The unemployment rate differential is driven by the fact that workers withoutVET face harsher labour market conditions, both in terms of higher job destruction (0.058versus 0.034 for those with VET) and lower job offer arrival rates (0.84 offers per yearversus 1.06 offers per year for those with VET). Moreover, when considering workers’welfare, we find that the average welfare of those without VET is around one third lowerthan the one of their similarly able peers with VET. Not only are workers with compul-sory education more likely to find themselves in unemployment, but their welfare both in

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unemployment and when employed is much lower.

6.3 A simple cost-benefit analysis

Table 8 presents the estimated yearly costs and benefits of VET for workers, firms, andthe Swiss state in 2009. Our framework allows us to compute the net benefits for workersand firms. The benefits of workers are calculated as the difference in annual earnings be-tween VET workers with skills and VET workers without skills (lower bound estimate) orworkers without VET (upper bound estimate) shown in Tables 6 and 7. The net benefitsof firms are computed from the annual profit on VET workers (upper bound estimate) -as productivity minus wage - or the difference in annual profits between VET workersand non-VET workers (lower bound estimate). Given that our data does not contain anyinformation about the costs of VET, we draw on VET cost estimates from the FederalOffice of Statistics of Switzerland for the State and firms (lower bound cost estimate forfirms)23 and a survey among firms on VET training costs in 2009 by Strupler and Wolter(2012) (upper bound cost estimate for firms).24

Table 8: Cost-benefit analysis of VET in 2009 (in mio CHF)Costs Benefits

Workers 10,196 to 18,360Firms 2,754 to 5,350 -11,165 to 75,829State (incl. cantons) 3,560Total 6,314 to 8,910 -969 to 94,189

Our results show that the benefit of all workers with VET amounts to 10 to 18 bil-lion Swiss Francs a year. The estimated net benefits for firms ranges from -11 billion tomore than 75 billion, the result of two different counterfactual scenarios. In the first sce-nario (upper bound estimate), we assume that the jobs which are filled with VET workerswould not exist otherwise and hence, the annual profit on VET jobs are the net benefit.In the alternative scenario (lower bound estimate), all jobs of the firm could be filled withnon-VET workers, though with the productivity and wages of non-VET workers. The netbenefit in this second scenario is negative (-11 billion), as the hourly net profit on VET

23These numbers are published by the Federal Office of Statistics as part of the statistics on public educationexpenditures (only in German and French) on https://www.bfs.admin.ch/bfs/de/home/statistiken/bildung-wissenschaft/bildungsindikatoren/indikatoren/ausgaben-berufsbildung.assetdetail.4182700.html (accessedonline on June 1, 2018).

24Notice that these costs overestimate the net costs of VET for firms, as they do not factor in the productivityof VET workers during their training (but includes their wages as costs). For two out of three firms, theseproductivity gains outweigh the costs of VET for firms over the duration of the apprenticeship as shown inWolter et al. (2006).

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workers is lower (49.1−35.9 = 13.2 CHF) than for non-VET workers (47.2−31.5 = 15.7

CHF).25 Whether the overall benefit of VET outweighs its cost or not (and by how much)depends crucially on the alternative production options of firms without the VET sys-tem.26 However, workers stand to benefit massively from VET and the overall benefit ofa VET system can potentially be very large.

7 Conclusion

This paper provides a structural examination of the Swiss labour market for workers whograduated from vocational education and training (VET) in Switzerland and studies howtheir wages and employment are determined simultaneously. We distinguish workers whohave acquired different bundles of interpersonal, cognitive and manual skills in VET pro-grammes. We analyse empirically how their skills affect job offers, wages and unemploy-ment using a simple search and matching framework. Under the assumption that matchproductivity exhibits worker-job complementarity for each of these skills, we identify andestimate the demand of firms for interpersonal, cognitive and manual skills and their in-teractions.

We find that the demand for (and hence, returns to) cognitive skills dominates the de-mand for interpersonal and manual skills. The average productivity of cognitive skills isalmost twice as high as the one of interpersonal and manual skills. The finding of largerreturns in wages to cognitive skills than non-cognitive skills is in line with the resultsby Lise and Postel-Vinay (2016) and Lindqvist and Vestman (2011) reported for the USand Sweden, respectively. Moreover, we also find evidence of complementarity betweencognitive and interpersonal skills, and evidence of firms specialising either in manual ornon-manual jobs. The high demand for complementarity in cognitive and interpersonalskills is also mirrored (though to a weaker extent) by the supply of skill bundles by work-ers, indicating that the supply of VET skills matches the demand for these skills.

For workers with a VET degree, the average returns to VET skills amount to 9%in hourly wages according to our simulation results. Furthermore, obtaining a VET de-

25To obtain firms’ net benefit, we multiply the hourly net profit with the respective employment shares of96.8% and 93.5%, respectively, and with annual working hours of 2,040. The average productivities andwages are shown in Table 6.

26This finding is similar to Wolter et al. (2006) who find a large heterogeneity in benefits (and costs) for firmsto provide vocational training for apprentices. While Wolter et al. (2006) provide a cost-benefit analysis forthe duration of the apprenticeship, our analysis attempts to measure the benefits of the VET system for thewhole economy beyond the training period.

31

gree improves labour market opportunities of workers through higher job arrival rates andlower job destruction. Overall, workers reap large benefits from VET, while the benefitsfor firms cannot be as easily narrowed down and depend on the assumptions in the coun-terfactual scenario.

Our analysis also reveals that workers who only get compulsory education could ex-pect returns to a VET degree of around 11% in hourly wages and their welfare wouldincrease by one third through better labour market opportunities. In this exercise we takeinto account that workers with only compulsory education have lower cognitive abiliti-ties, but we show that they are nonetheless comparable to workers with a VET degree incertain occupational skill groups. This warrants further attention from policy makers.

Our model and estimation come with a number of limitations. We make some para-metric assumptions on the match productivity to identify and estimate the demand for eachskill from observed wage distributions. In spite of these limitations, our model achieves afairly good fit of the wage moments observed in the data, while unemployment rates areslightly less well matched (though they are also less precisely measured in the data).

32

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35

A Selection into vocational and general educationIn this Appendix we present some evidence on selection into vocational and general upper sec-ondary education in Switzerland in the early 2000s. To do so, we rely on the TREE longitudinalstudy, which followed the careers of Swiss participants of the PISA assessment in 2000. The in-terest in this data set lies in its information about the standardised PISA test scores, (self-assessed)personality traits and education choices of students at the end of their compulsory schooling (after9 school years at age 16 approximately) and in subsequent waves. The TREE data set only coversworkers of one cohort and hence, the sample size of this data set is much smaller than the SESAMdata set used in our main analysis.27 However, it is well suited to document pattern of initial se-lection into different education tracks.

Figure A.1 presents the distribution of cognitive abilities (as measured by PISA scores inreading and math in 2000) and self-assessed personality traits (persistence, locus of control andambition in 2001) for male students who either selected into a 3- or 4-year VET track, into generalupper secondary education (general education) or who were not enrolled in any further educationprogramme (compulsory education) one year after graduating from compulsory lower secondaryeducation (9 years of education). Those selecting a VET track are split into those who only com-plete vocational education (denoted by ’only vocational education’), and those who will completevocational education and eventually enroll into tertiary education within 10 years after graduatingfrom lower secondary education (denoted by ’vocational + tertiary education’).

Students in the vocational education track have on average lower cognitive abilities than thosein the general education track, but higher than those with only compulsory education. It is im-portant to note that students with vocational education are heterogeneous: Students who onlycomplete vocational education are more comparable to those with compulsory education than totheir peers in vocational education who will eventually enroll in tertiary education. In terms ofpersonality traits, differences across education tracks are less stark. For locus of control and am-bition, the respective distributions differ only marginally. For persistence, we find that students inthe vocational and general education track are on average more persistent than those who do notgo beyond compulsory education.

27There is also non-negligeable sample attrition from one wave to the next.

36

Figure A.1: Selection into compulsory, vocational and general education

(a) PISA reading score (b) PISA math score

(c) Persistence (self-assessed) (d) Locus of Control (self-assessed)

(e) Ambition (self-assessed)Notes: Standardised PISA reading and math scores lie between 0 and 1. Personality traits ’Persistence’, ’Locus of control’ and

’Ambition’ are the average over a number of ordinal survey questions relative to each trait which can take on value 1 ’not at all true’,2 ’hardly true’, 3 ’moderately true’, and 4 ’exactly true’.

37

Table A.1 provides summary statistics for PISA scores (reading, math) and personality traitsby education tracks (upper panel), as well as by occupation cluster for those within the vocationaleducation track. It also gives the share of each occupation cluster who will enroll in tertiary edu-cation within 10 years.

Breaking up the vocational education track into VET occupation clusters which differ in theirskill mix reveals a large heterogeneity across clusters. Students in some VET occupations (like oc-cupation cluster 11 with intermediate interpersonal, low manual and intermediate cognitive skills,or cluster 14 with low interpersonal, high manual and intermediate cognitive skills) have on av-erage the same cognitive abilities as those with only compulsory education. In contrast, studentsin other VET occupations (like cluster 10 with intermediate interpersonal, low manual and highcognitive skills) resemble on average quite closely students in general education in terms of theircognitive abilities and personality traits. Their rate of enrolling in tertiary education within 10years is also much higher than the one of the former groups.

Overall, we find that the distributions of personality traits and cognitive abilities of students in

different education tracks overlap to a large extent. This suggests that students in the vocational

education track at the lower ability end resemble those who only get compulsory education, while

those at the higher end are as good as those who pursue a general education track. By focussing

our analysis only on students who complete vocational education but do not eventually enroll in

tertiary education, we limit the issue of selection on ability to a considerable degree.

38

Tabl

eA

.1:

PIS

AS

CO

RE

SA

ND

PE

RS

ON

AL

ITY

TR

AIT

S

PISA

read

PISA

mat

hPe

rsis

tenc

eL

ocus

ofco

ntro

lA

mbi

tion

Enr

olli

nO

bsM

ean

Std.

Obs

Mea

nSt

d.O

bsM

ean

Std.

Mea

nSt

d.M

ean

Std.

tert

iary

Com

puls

ory

educ

atio

n77

0.44

0.09

390.

500.

0948

2.88

0.62

2.94

0.59

2.81

0.69

Voca

tiona

ledu

catio

n(a

ll)1,

311

0.49

0.08

697

0.54

0.09

1,08

03.

150.

483.

010.

422.

990.

6316

.6%

ofw

hich

:on

lyvo

catio

nal

1,09

30.

480.

0858

00.

530.

0989

03.

150.

493.

000.

432.

960.

62of

whi

ch:

voca

tiona

l+te

rtia

ry21

80.

540.

0711

70.

600.

0719

03.

140.

483.

040.

393.

120.

64G

ener

aled

ucat

ion

689

0.56

0.07

373

0.61

0.08

585

3.05

0.51

3.05

0.46

2.87

0.65

Voca

tiona

ledu

catio

nby

occu

patio

ncl

uste

rH

-int

erpe

rson

alH

-cog

nitiv

e0

00

H-m

anua

lM

-cog

nitiv

e0

00

L-c

ogni

tive

30.

500.

071

0.53

03

3.53

0.31

3.33

0.58

3.17

0.29

n.a.

H-c

ogni

tive

390.

500.

0920

0.55

0.06

292.

990.

572.

880.

432.

870.

678.

1%L

-man

ual

M-c

ogni

tive

500.

480.

0828

0.52

0.08

443.

100.

592.

960.

562.

950.

664.

0%L

-cog

nitiv

e0

00

M-i

nter

pers

onal

H-c

ogni

tive

10.

55n.

a.0

13.

2n.

a.2.

4n.

a.2.

5n.

a.n.

a.H

-man

ual

M-c

ogni

tive

210.

450.

0614

0.55

0.05

183

0.38

3.11

0.33

3.06

0.66

0%L

-cog

nitiv

e26

0.48

0.08

130.

490.

0920

3.13

0.52

2.94

0.46

3.13

0.67

11.5

%H

-cog

nitiv

e14

40.

540.

0776

0.59

0.09

115

3.05

0.51

2.99

0.49

2.93

0.65

31.3

%L

-man

ual

M-c

ogni

tive

380.

440.

0723

0.50

0.08

313.

270.

493.

010.

442.

970.

605.

3%L

-cog

nitiv

e99

0.49

0.08

470.

560.

0983

3.14

0.53

3.07

0.40

2.94

0.68

23.2

%

L-i

nter

pers

onal

H-c

ogni

tive

570.

470.

0935

0.51

0.11

453.

210.

443.

060.

383.

060.

657.

0%H

-man

ual

M-c

ogni

tive

500.

420.

1020

0.48

0.09

383.

250.

573.

010.

552.

930.

724.

0%L

-cog

nitiv

e38

0.47

0.08

220.

500.

0931

3.19

0.45

3.08

0.49

2.95

0.61

10.5

%H

-cog

nitiv

e5

0.52

0.07

10.

57n.

a.3

3.33

0.31

3.07

0.31

3.33

0.76

20.0

%L

-man

ual

M-c

ogni

tive

320.

450.

0821

0.54

0.08

233.

300.

423.

070.

313.

230.

616.

3%L

-cog

nitiv

e18

0.49

0.07

100.

540.

0718

3.29

0.41

3.06

0.43

3.06

0.66

11.1

%

Voca

tiona

ledu

catio

n(m

atch

ed)

619

0.49

0.09

329

0.54

0.09

501

3.15

0.51

3.02

0.45

2.98

0.65

Not

es:

Stan

dard

ised

PISA

read

ing

and

mat

hsc

ores

liebe

twee

n0

and

1.Pe

rson

ality

trai

ts’P

ersi

sten

ce’,

’Loc

usof

cont

rol’

and

’Am

bitio

n’ar

eth

eav

erag

eov

era

num

bero

ford

inal

surv

eyqu

estio

nsre

lativ

eto

each

trai

tw

hich

can

take

onva

lue

1’n

otat

all

true

’,2

’har

dly

true

’,3

’mod

erat

ely

true

’,an

d4

’exa

ctly

true

’.’T

ertia

ry’

deno

tes

the

shar

ew

hoen

roll

inte

rtia

ryed

ucat

ion

with

in10

year

sof

grad

uatin

gfr

omco

mpu

lsor

yed

ucat

ion.

39

B Comparison of skill measures for Swiss VET occupa-tions with O*Net-based measures

Table B.1: CORRELATIONS BETWEEN SKILL MEASURES.interp. (VET) manual (VET) cogn. (VET) interp. (O*Net) manual (O*Net) cogn. (O*Net)

interpersonal (VET) 1.0000

manual (VET) -0.9098 1.0000(0.0000)

cognitive (VET) 0.2826 -0.5007 1.0000(0.0044) (0.0000)

interpersonal (O*Net) 0.4860 -0.4957 0.1801 1.0000(0.0000) (0.0000) (0.0729)

manual (O*Net) -0.2467 0.2564 -0.1434 -0.2456 1.0000(0.0134) (0.0100) (0.1546) (0.0138)

cognitive (O*Net) 0.0889 -0.2708 0.3556 0.2096 -0.0099 1.0000(0.3793) (0.0064) (0.0003) (0.0363) (0.9222)

Notes: Correlation coefficients between skill measures based on BIZ list of skills required in training for VET occupations and skillsresulting from principal components analysis of skills, abilities, knowledge, work activity and work context in O*Net data. P-valuesin parentheses.

We validate our skill measures by comparing them to corresponding measures constructedfrom the O*Net database. For 100 out of 220 VET occupations we observe the corresponding oc-cupation in the O*Net data set, for which we retrieve the O*Net measures for more than 200 skills,abilities, knowledge, work activities and work context. Similar to Lise and Postel-Vinay (2016),we perform Principal Component Analysis on these 200 variables and retain the three principalcomponents. We combine these three principal components and impose three exclusion restric-tions to interpret the measures as cognitive, manual and interpersonal skills: 1) the mathematicsscore only reflects cognitive skills, 2) the manual dexterity score only reflects manual skills, 3) thesocial perceptiveness score only reflects interpersonal skills. We then correlate these O*net skillmeasures with our corresponding skill measure derived from the BIZ list compiled by Zihlmannet al. (2012). The correlation coefficients thus obtained are: 0.25 (manual), 0.34 (cognitive), and0.48 (interpersonal), respectively. All correlations are statistically different from 0 at the 99% sig-nificance level.

This procedure confirms that the skills conferred in VET training in Switzerland correlatesignificantly with the skills used in corresponding occupations in the United States. There may,however, still be large differences between the skills of a Swiss carpenter and the skills of a UScarpenter. We retain our skill measures as they cover a larger set of VET occupations in our sampleand reflect more precisely the specific skills acquired in VET in Switzerland.

40

C Labour market transitions by occupational cluster

Table C.1: DESCRIPTIVE STATISTICS: TRANSITION RATES.Obs EE stay EE change UE EU UU

H-interpersonal

H-cognitive n.a. n.a. n.a. n.a. n.a. n.a.H-manual M-cognitive n.a. n.a. n.a. n.a. n.a. n.a.

L-cognitive 774 0.882 0.063 0.016 0.023 0.016

H-cognitive 1,235 0.867 0.065 0.023 0.024 0.022L-manual M-cognitive 670 0.828 0.121 0.021 0.027 0.004

L-cognitive 164 0.793 0.091 0.030 0.055 0.030

M-interpersonal

H-cognitive 690 0.935 0.049 0.004 0.007 0.004H-manual M-cognitive 288 0.924 0.038 0.014 0.017 0.007

L-cognitive 279 0.889 0.075 0.014 0.018 0.004

H-cognitive 589 0.894 0.053 0.015 0.021 0.009L-manual M-cognitive 634 0.877 0.068 0.019 0.028 0.008

L-cognitive 1,098 0.859 0.080 0.025 0.020 0.018

L-interpersonal

H-cognitive 173 0.850 0.104 0.006 0.035 0.006H-manual M-cognitive 914 0.877 0.085 0.014 0.016 0.008

L-cognitive 374 0.912 0.043 0.016 0.013 0.016

H-cognitive 94 0.926 0.043 0.000 0.011 0.022L-manual M-cognitive 310 0.913 0.065 0.010 0.006 0.006

L-cognitive 223 0.906 0.058 0.013 0.018 0.004

all clusters 8,509 0.879 0.071 0.018 0.021 0.012

Compulsory schooling 2,225 0.887 0.051 0.027 0.022 0.015General upper secondary education 685 0.806 0.093 0.036 0.036 0.028

41

D Goodness of fit

42

Tabl

eD

.1:

GO

OD

NE

SS

OF

FIT

I:W

AG

ES

Mea

nho

urly

wag

eSt

d.de

v.ho

urly

wag

eL

owes

t1%

hour

lyw

age

Obs

erve

dSt

d.E

rror

Sim

ulat

edO

bser

ved

Std.

Err

orSi

mul

ated

Obs

erve

dSt

d.E

rror

Sim

ulat

ed

H-i

nter

pers

onal

H-c

ogni

tive

n.a.

n.a.

n.a.

n.a.

n.a.

n.a.

n.a.

n.a.

n.a.

H-m

anua

lM

-cog

nitiv

en.

a.n.

a.n.

a.n.

a.n.

a.n.

a.n.

a.n.

a.n.

a.L

-cog

nitiv

e37

.67

0.32

335

.19

10.6

40.

411

10.1

419

.20

0.42

718

.52

H-c

ogni

tive

40.1

40.

369

38.5

915

.43

0.38

012

.98

18.4

20.

304

18.4

7L

-man

ual

M-c

ogni

tive

33.8

90.

328

36.3

89.

910.

372

10.7

717

.97

0.27

418

.76

L-c

ogni

tive

29.6

20.

452

35.7

36.

520.

424

10.5

518

.13

0.63

018

.15

M-i

nter

pers

onal

H-c

ogni

tive

40.0

90.

339

36.5

010

.74

0.34

610

.15

20.9

90.

596

19.5

8H

-man

ual

M-c

ogni

tive

38.0

60.

630

35.4

212

.87

0.89

89.

6919

.27

0.65

319

.02

L-c

ogni

tive

33.7

30.

494

33.5

39.

770.

702

8.98

18.0

50.

429

18.0

1

H-c

ogni

tive

39.1

30.

417

37.7

511

.88

0.45

011

.18

19.2

70.

726

19.3

2L

-man

ual

M-c

ogni

tive

35.8

90.

303

35.4

99.

070.

299

9.61

18.2

30.

458

19.3

1L

-cog

nitiv

e36

.09

0.28

434

.14

11.2

20.

403

9.08

19.1

20.

314

18.6

6

L-i

nter

pers

onal

H-c

ogni

tive

33.7

40.

485

37.3

77.

860.

400

10.5

218

.91

0.70

620

.34

H-m

anua

lM

-cog

nitiv

e33

.41

0.21

635

.08

7.78

0.33

09.

2019

.06

0.40

319

.20

L-c

ogni

tive

33.8

40.

452

33.7

510

.33

0.85

48.

9818

.44

0.48

718

.74

H-c

ogni

tive

40.5

10.

983

36.2

511

.21

1.27

110

.00

21.8

62.

263

19.0

6L

-man

ual

M-c

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tive

33.8

20.

444

34.9

38.

850.

879

8.94

18.0

30.

611

19.7

8L

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nitiv

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0.48

333

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8.44

0.51

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6518

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0.92

218

.42

43

Tabl

eD

.2:

GO

OD

NE

SS

OF

FIT

II:U

NE

MP

LO

YM

EN

TA

ND

LA

BO

UR

MA

RK

ET

TR

AN

SIT

ION

S

Une

mpl

oym

entr

ate

EU

rate

UE

rate

Obs

erve

dSt

d.E

rror

Sim

ulat

edO

bser

ved

Std.

Err

orSi

mul

ated

Obs

erve

dSt

d.E

rror

Sim

ulat

ed

H-i

nter

pers

onal

H-c

ogni

tive

n.a.

n.a.

n.a.

n.a.

n.a.

n.a.

n.a.

n.a.

n.a.

H-m

anua

lM

-cog

nitiv

en.

a.n.

a.n.

a.n.

a.n.

a.n.

a.n.

a.n.

a.n.

a.L

-cog

nitiv

e0.

039

0.00

50.

037

0.02

40.

006

0.02

30.

500

0.10

40.

643

H-c

ogni

tive

0.04

70.

005

0.03

20.

025

0.00

50.

022

0.50

90.

068

0.65

5L

-man

ual

M-c

ogni

tive

0.03

00.

005

0.02

90.

027

0.00

60.

018

0.81

30.

101

0.65

0L

-cog

nitiv

e0.

082

0.01

70.

032

0.05

80.

019

0.02

10.

500

0.16

70.

638

M-i

nter

pers

onal

H-c

ogni

tive

0.01

80.

004

0.03

40.

009

0.00

40.

021

0.50

00.

224

0.65

1H

-man

ual

M-c

ogni

tive

0.02

40.

007

0.02

80.

018

0.00

80.

021

0.66

70.

211

0.56

5L

-cog

nitiv

e0.

027

0.00

80.

037

0.01

80.

008

0.01

90.

800

0.20

00.

669

H-c

ogni

tive

0.04

00.

006

0.03

40.

028

0.00

70.

021

0.77

80.

101

0.64

7L

-man

ual

M-c

ogni

tive

0.04

00.

006

0.03

30.

029

0.00

70.

020

0.72

20.

109

0.72

3L

-cog

nitiv

e0.

048

0.00

50.

031

0.02

30.

005

0.02

20.

542

0.07

30.

663

L-i

nter

pers

onal

H-c

ogni

tive

0.03

30.

010

0.03

00.

035

0.01

40.

024

0.50

00.

500

0.68

4H

-man

ual

M-c

ogni

tive

0.03

30.

005

0.03

40.

017

0.00

40.

022

0.65

00.

109

0.62

7L

-cog

nitiv

e0.

035

0.00

70.

030

0.01

40.

006

0.01

80.

500

0.15

10.

606

H-c

ogni

tive

0.02

00.

012

0.03

20.

011

0.01

10.

022

0.00

00.

100

0.61

8L

-man

ual

M-c

ogni

tive

0.02

20.

007

0.02

90.

007

0.00

50.

020

0.50

00.

224

0.56

7L

-cog

nitiv

e0.

025

0.00

80.

030

0.02

30.

010

0.01

50.

750

0.25

00.

643

44

E Estimation results: Compulsory education

Table E.1: ESTIMATED PARAMETERS (COMPULSORY EDUCATION)

General productivity

Estimate Std. Err.

µ0: Location 3.81 n.a. Mean: 47.25σ0: Scale 0.31 n.a. Variance: 219.44

Offer and destruction rates

λ: Offer arrival rate 0.844 n.a.η: Destruction rate 0.058 n.a.

Flow value of unemployment

b0: Unemployment flow -254.35 n.a.

45